Question

please answer this
Triangle ABC is a right angled triangle in which angle C is a right angle . A perpendicular CD is drawn from vertex C to intersect ABat D prove that 1/CD^2=1/BC^2+1/CA^2 ​

Answer 1

Answer:

Hope this helps...

In your diagram, triangles ABC and CBD are similar, since they have a common angle at B and they both have a right angle (at C in ABC, and at D in CBD).

So

AB / AC = BC / CD

=> 1 / CD = AB / ( AC × BC )

=> 1 / CD² = AB² / ( AC² × BC² )

                = ( AC² + BC² ) / ( AC² × BC² )            [ by Pythagoras' Theorem ]

                = 1 / BC²  +  1 / AC²